Flame propagation in solids and high-density fluids with Arrhenius reactant diffusion

Abstract

The combustion of solids and high-density fluids, such as the combustion synthesis of refractory materials or the high-pressure oxidation of organic compounds in supercritical water, is often characterized by a highly temperature-dependent mass diffusivity. In particular, the case of an Arrhenius dependence of this quantity on temperature is considered, where the activation energy of reactant diffusion is of the same order as that of the overall chemical reaction. Exploiting the asymptotic limit of large activation energies, it is shown that reactant diffusion becomes significant in the thin reaction zone, where a balance among convection, reaction, and diffusion is maintained. Relative to the case of either a zero or constant mass diffusion coefficient, this leads to modifications in the steady, planar flame-speed eigenvalue. A new asymptotic model is then derived that predicts corresponding shifts in the neutral stability boundary that marks the transition from steady to nonsteady modes of flame propagation.